Technical Trading Rules compared against actual NASDAQ100 performance

1. TECHNICAL TRADING RULES FOR THE NASDAQ 100
FINC 6364
University of Houston-Victoria
Fall 2013
Ramon Lozada
Temiloluwa Vasco

2. 1
Table of Contents
Abstract...........................................................................................................................................2
Introduction....................................................................................................................................3
Data and Methodology ..................................................................................................................4
Empirical Results...........................................................................................................................6
Trading Strategies..........................................................................................................................6
Statistical Results for Trading Strategy......................................................................................10
Break-Even Trading Costs for Selected Strategy.......................................................................11
Conclusions...................................................................................................................................11
References.....................................................................................................................................12

3. 2
ABSTRACT
This paper analyzes the behavior of moving average technical trading rules applied to 15
years of the NASDAQ 100 Index. It is found that the differences between conditional resources
during buy and sell periods has changed dramatically over the previous 14 years relation to the
previous years of data, but differences in conditional variances have not changed much over the
entire sample. Further strength forms indicate that similar results could be obtained with simple
momentum based strategies. The analysis is performed on the actual NASDAQ 100 series, but
these techniques could be useful in derivative markets where better estimates of conditional
resources and variances would be useful information.
The sole use of price and related summary statistics in a technical trading strategy is a
strong procedure for market efficiency. In practice, however, traders vigorously use technical
analysis to make investment decisions which makes this an important, but often mistreated, area
for revision. This paper includes some experimental sections, which provide important evidence
on the profitability of technical trading. The results from the detailed analysis undertaken in this
paper have general applicability for investment. Using a very large model of high frequency
data, a detailed evaluation of the profitability of our selected trading strategy is performed.

4. 3
Introduction
The ability of simple rules to predict asset price movements, or technical analysis, has
been a controversial subject for many years. While the academic community has generally held
technical analysts in disdain, its recent fascination with predictability has reopened many of the
old cases against technical analysis. The evidence seems somewhat questionable on the
usefulness of the rules, but this is in contrast to the earlier results that suggested that anyone
following these was less than logically interested in them. To the users and investors, technical
trading rules can be viewed as simply another set of moment conditions that can either be used in
specification testing, or in estimation. They, therefore, play a dual role as an interesting behavior
which might have some practical value, and are a data description that financial thinkers should
be aware of.
This paper examines the NASDAQ 100 with respect to simple moving average rules.
Using the NASDAQ 100 shows that moving average technical trading rules had some predictive
abilities in both conditional means and variances. Furthermore, they showed that these results
were relatively stable over their 15 year sample period. This important result raises some
questions about trading rules, and the stationary of financial time series. When analyzed in light
of moving average trading rules, some very interesting similarities and differences appear.
First, analysis is performed on conditional variances as well as conditional means.
Secondly, some further strength verification is performed on the selected trading rules.
Specifically, a simpler momentum based dynamic strategy appears to be very similar to the
moving average rules. The tests implemented in this paper are concerned with the money market
when we are not invested in the market. Also, it is obvious that a useful forecast of market
changes might provide better dynamic trading strategies in index markets.

5. 4
Data and Methodology
We use DataStream’s daily index prices of the NASDAQ 100 from November 13th
1998
to November 12th
of 2013. We compute daily returns as changes in logarithms of the stock index
level. We estimate approximate annualized returns on the basis of 260 trading days per year as
exponential of (260R) –1, where R is the average daily return. To estimate daily interest rate, we
use DataStream’s daily annual interbank rate and divide the daily one-month rate by 365.
The 365 day denominator was selected in order to avoid overestimating the returns of various
trading strategies when compared to the buy-and-hold strategy.
Technical analysis is the study of market action, primarily through the use of charts, for
the purpose of forecasting future price trends (Murphy, 1999). It is based on the idea that prices
move in trends which are determined by the traders’ attitude towards various economics,
political and psychological forces. “The art of technical analysis is to identify trend changes at an
early stage and to maintain an investment posture until the weight of evidence indicates that the
trend has reversed” (Pring, 1991). Two of the most important techniques used to determine
market trends are based on the crossing of three moving averages (MA) of stock prices and
market price momentum.
According to moving average rule, buy (sell) signals are emitted when the short short-
term moving average exceeds (is less than) the intermediate term average, which in turn exceeds
(is less than) the long-term average by a specified percentage. In this study we use long moving
averages of 4, 9 and 18. The use of three moving averages is considered conservative, especially
when used in conjunction with Momentum, which generates buy (sell) signals when the
momentum is increasing and greater (less) than 0.

6. 5
We define Pt as the short moving average or the raw index level at time t, and define long
moving average of M at time t as:
‫ܣܯ‬௧ሺ‫ܯ‬ሻ =
ଵ
ெ
∑ ܲ௧ି௜
ெିଵ
௜ୀ଴ (1)
We will test the triple moving average rule (TMA) in conjunction with the Momentum
rule. As for trading the index, we will be either in the market (buy days) or out of the market (sell
days). We assume that a trader following these MA strategies could presumably observe the
prices a few minutes prior to the day’s close and make the trading decision at the close. If the
MA4 is above the MA9, and the MA9 is above the MA18, then the trader will be in the market
the next day by buying the index at the previous day’s closing price (next day will be a buy day).
Next day’s return will be the difference between the logarithm of the closing price next day and
the logarithm of closing price the previous day. On the other hand, if the If the MA4 is below the
MA9, and the MA9 is below the MA18, then we will sell the index at the closing price and will
be out of the market next day (sell days). The momentum is used as a secondary indicator for
those times when the TMA does not provide a clear buy or sell signal. When momentum
increases from negative (MM<0) in the previous day to positive (MM>0) in the current day, the
trader will buy the index at the closing price and will be in the market the next day. Conversely,
when momentum decreases from positive in the previous day (MM>) to negative in the current
day (MM<0), the trader will sell the index at the closing price and be out of the market the next
day. Should either the TMA or the MM not provide clear signals of changing conditions, the
trader will maintain the previous day’s position which was taken with a clear signal from the
TMA and/or the MM. We define mean buy and mean sell returns as follows:
ܺሺܾሻ =
ଵ
ேሺ್ሻ
∑ ܴ௕ (2)

7. 6
ܺሺ‫ݏ‬ሻ =
ଵ
ேሺೞሻ
∑ ܴ௦ (3)
Where, N(b) and N(s) are total number of buy and sell days and Rb and Rs are daily returns of buy
and sell days. We will test whether the returns of the triple moving average trading rules, used in
tandem with the momentum rule are greater than a buy and hold strategy and whether the mean
buy is different than the mean sell. More specifically:
H0 : X(b) - X(h) =0, X(s)-X(h) = 0 , X(b) – X(s) =0
HA: X(b) – X(h) ≠ 0, X(s) – X(h) ≠ 0, X(b) – X(s) ≠ 0
Where X(h) is the mean return for the buy-and-hold strategy. The test statistic for the mean buy
returns over the mean buy-and hold strategy is:
‫ݐ‬ =
௑ሺ௕ሻି௑ሺ௛ሻ
ඥ௏௔௥ሺ௕ሻ ே್⁄ ା ௏௔௥ሺ௛ሻ ே⁄
(4)
where Var(b) and Var(h) are the variance of buy and buy-and-hold returns respectively. The
above formula is also used to test the mean sell returns over the mean buy-and-hold strategy; and
the mean buy returns over the mean sell returns by replacing the appropriate variables in the t-
statistic formula.
Empirical Results
For the entire period the daily average of buy-and-hold strategy is 0.0000915309
(.009153 percent per day) with a standard deviation of 0.0000835774. The t-value for the buy
and hold strategy for the entire period (3895 observations) is equal to 0.82 (.00915309 divided
by .0000835774 / root square of 3895).
Table I
Statistical Results for Standard Moving Average Rules
Results for daily data from 11/13/1998 to 11/12/2013. Rules are identified as (Buy or Sell) where buy
and sell are from the triple moving averages trading rule. Nb and Ns are the number of buy and sell

8. 7
signals reported in each period. SDb and SDs are standard deviation of buy and sell signals, respectively.
The numbers in the parentheses are the t-statistics testing the difference of the mean buy and mean sell
from the unconditional 4-day mean, and buy-sell from zero.
Rules Buy Sell Buy - Sell SD/ Buy SD/ Sell N/buy N/sell
MA(4,9,18) 0.0002469004
(0.4641296206)
0.0000943758
(0.0049698260)
0.000152525
(0.2300097078)
0.0156691067 0.0236295250 2191 1704
Table I summarizes the results of standard triple moving average trading rules. We report
mean returns on buy days and sell days, standard deviations of returns on buy and sell days, and
total number of buy and sell days. The numbers in the parentheses are the t-statistics (equation 4)
testing the difference of the mean buy and mean sell from the unconditional 1-day mean, and
buy-sell from zero. Table I reports results of trading rule of MA4>MA9>MA18 in tandem with
MM Today-1<0 MMToday >0; we will be in the market (buy days). The opposite applies to Sell
days: MA4<MA9<MA18 in tandem with MM Today-1>0 MMToday <0; then we are out of the
market. If any of the trading rules are violated, we maintain our previous position, until either
trading rule applies.
The buy-sell differences (column 4) are positives but the t-statistics for these differences
are not significant, rejecting the alternative hypothesis of inequality with zero. The mean buy and
sell returns are shown in columns 2 and 3.
The t-values for mean buy and mean sell are not significant, rejecting the alternative
hypothesis. On the average, the t-values for buy days, sell days, and buy minus sell days are not
significant, rejecting the inequality of mean buy with zero, mean sell with zero, and mean buy
with mean sell. The standard deviations of buy days and sell days are reported in Columns 5 and
6. The standard deviations for buy days are smaller than those for sell days. This implies that the
market is less volatile for buy periods than sell periods. Columns 7 and 8 report the number of

9. 8
buys and sells for various rules. On the average, according to our trading rule, our system will be
2,191 days in the market and 1,704 days out of the market.
If technical analysis did not have any power to forecast price movements, then we should
observe that the buy days returns do not differ appreciably from sell days returns, or the mean
buy day should not be significantly different than the mean sell days. The results of Tables I
indicate that the mean buy days are not significantly different from the mean sell days for both
sample and increasing moving average rules. Given the very strong results of Tables I and II, we
conclude that technical trading could not work and could not be superior to buy and hold
strategy.
Trading Strategies
We next provide some information on the degree to which traders using these technical
trading rules can earn trading profits that could beat the buy-and-hold strategy. Given that the
mean buy is greater than both the mean sell and the unconditional 1-day mean, the profitability
of technical trading rules depends on trading strategy, especially, what position should the trader
take when the rule emits sell signals. If the trader does not invest on the sell days, then the
trader’s return on the sell days will be zero which will result in a mean return of (Nb/N)*X(b) +
(Ns/N) *0 for this strategy.
In this study we selected the strategy where the trader will be in the stock market when
trading rules emit buy signals and be in the money market when it emits sell signals
(Long/Money Market). We estimate the daily return for the strategy and subtract from it the daily
return from buy-and-hold strategy to get the daily difference return. To test whether the average
daily difference is greater than zero, we express the null and alternative hypotheses as follows:
H0 : ddif = 0

10. 9
HA: ddif ≠0
The t-statistic for the above test is:
‫ݐ‬ =
௑ሺௗௗ௜௙ሻ
ඥ௏௔௥ሺௗௗ௜௙ሻ ே⁄
(5)
where X(ddif) is the average daily difference of returns of each strategy over the buy-and-hold
strategy, Var(ddif) is the variance of daily difference returns, and N is the total number of days.
Table III below reports the results of the selected strategy for the TMA rules used in
tandem with Momentum rules.
Table II
Statistical Results for Trading Strategy
X(ddif) and SD(ddif) are average and standard deviation of daily
difference between the return of the selected strategy and the buy-
and hold strategy. The numbers in the parentheses are the t-statistics
testing the equality of average daily difference from zero. Numbers
significant at the 5% level are marked with asterisks.
Strategy: Long/Money Market
Rule X(ddif) SD(ddif)
SMA (4,9,18) + Momentum -0.0000007
-0.0027
0.01562783
As shown in Table III, the strategy did not beat the buy and hold strategy; the average t-
values, -0.0027 is not significant, rejecting the alternative hypothesis that the average daily
difference is not equal to zero. The average standard deviations are .01562783, similar to the buy
and hold strategy standard deviation of 0.0195682. Therefore, the strategy has similar average
returns risks; they are in line with the market as implied by their low and insignificant t-values.
In conclusion, we have a strategy based on technical trading and they do not produce
results significantly different from the buy and hold strategy. Although the discovery of
profitable trading rules may be helpful in understanding market dynamics, traders would not be
able to exploit these rules without considering transaction costs. In order to account for

11. 10
transaction costs for the strategy, we report in Table IV below, the “break-even” transaction
costs, which are the one-way percentage cost that eliminates the additional return (if any) from
technical trading rules. We also report annual transaction costs assuming that one-way
transaction cost is 0.5 %.
Table III
Break-Even Trading Costs for Selected Strategy
X(ddif) is average daily difference between the return of strategy 2 (leverage/money) and the buy-and-
hold strategy from table IV. Annual Excess return is EXP(X(ddif) times 250) -1. Total trades represent the
number of total trades or total switch from in and out of the market. Trade per year is total trades divided
by number of years. Break-even costs are estimated by the ratio of annual excess return over trades per
year. Annual costs are estimated assuming one-way transaction cost of 0.5 %.
Strategy: Long/Money Market
Rule X(ddif)
Annual
Excess
Return %
Total
Trades
Trades
per
year
One way
Break-even
Costs %
Annual Cost
% Cost per
trade = 0.5%
SMA (4,9,18) + Momentum -0.0000007 -0.0168% 416 27.73 -0.0011% 7.5041%
The first column of Table IV identifies trading rules; the second column is the average
daily difference returns between the strategy one (Long/money) and the buy and hold strategy. In
column 3, we obtain the annualized excess returns as exponential of (excess return * 250) –1.
Column 4 reports total trades, numbers of in and out of the market signals, or total frequency of
transactions, implied by a specific trading rule. In column 5, we report average trade per year; or
total trades divided by 15.01 years, the number of years under consideration. Column 6 reports
one-way “break-even” transaction cost; or annual excess return divided by average annual trades.
One-way transaction cost is assumed to be the same for buying and selling the index. Finally, in
the last column we estimate annual transaction costs assuming that one-way transaction cost is
0.5 %. We believe our choice of 0.5% one-way transaction cost to be very conservative and
realistic based on lower estimates ranging between 0.24% to 0.26% provided by Bessembinder
& Chan (1995), Knez & Ready (1996) and Kroner (1995).

12. 11
Conclusions
Several papers have recently presented evidence that some simple trading rules are useful
for predicting stock market returns. In this paper we investigate the triple moving average trading
rules used in conjunction with the momentum trading rules for the Nasdaq 100 over the period of
11/13/1998 – 11/12/2013. Overall results do not provide support for the technical trading rules
that we explored over the buy and hold strategy.
If technical analysis does not have any power to forecast price movements, then we
should observe that the buy days returns do not differ appreciably from sell days returns. Our
results show that almost all buy-sell differences are negligible and the t-stats for these differences
are not significant, rejecting the alternative hypothesis of a difference between buy days returns
with sell days returns. Our results indicate that the triple moving average rule, used in
conjunction with the momentum rule, does not have predictive power and could not discern
recurring-price patterns for profitable trading.
We asked whether we could design a trading strategy to beat the buy-and-hold strategy
over the period under consideration, despite the non-predictive power of technical analysis from
analysis. We developed a strategy and tested it, noting that our results support the hypothesis that
technical trading rules do not outperform the buy-and-hold strategy.
Although the discovery of trading rules may be helpful in understanding market
dynamics, traders must also consider transaction costs. We calculated the break-even one-way
trading costs for both strategies, which significantly beats the buy and hold strategy over the
15.01-year period. Our results for the breakeven cost are small compared to the estimated actual
trading costs of 0.5 %. We conclude that technical trading rules do not have predictive power and
when used to design a trading strategy will produce results similar to the buy-and-hold strategy

13. 12
in the Nasdaq 100 stock market. The observation that technical trading rules do not have
predictive power for changes in the stock market is consistent with the efficient market theory.

14. 13
References
Murphy, John J. 1999. Technical Analysis of the Financial Markets. New York Institute of
Finance, New York, New York.
Pring M.J., Technical Analysis: Explained, McGraw-Hill Co., 1991.
Bessembinder H. and Chan K., “The Profitability of Technical Trading Rules in the Asian Stock
Markets, Pacific-Basin Finance Journal, 1995, 3, pp. 257-284
Knez P.J. and Ready M.J., “Estimating the Profits from Trading Strategies” Review of Financial
Studies, 1996, 9, pp. 1121-64.
Kroner, K., “Comments on: Do the profits from Technical trading Rules Reflect Inefficiencies?”,
mimeo, Wells Fargo Nikko Investment Advisors Advanced Strategy Group, San
Francisco 1995.